SKEDSOFT

Predictor Method : A general set of methods for integrating ordinary differential equations. Predictor-corrector methods proceed by extrapolating a polynomial fit to the derivative from the previous points to the new point (the predictor step), then using this to interpolate the derivative (the corrector step).

All predictor methods are explicit methods.

We have k data values, (x_i, f_i)(x_{i– 1}, f_i–1), ..., (x_{i–k 1}, f_{i–k 1}). For this data, we fit the Newton’s backward difference interpolating polynomial of degree k – 1

.....................1.1

Note that,

The expression for the error is given by

..................1.2

where ξ lies in some interval containing the points x_i, x_i–1, ..., x_{i–k 1} and x. We replace f(x, y) by
P_k–1(x) in

............................1.3

 The limits of integration in (1.3) becomefor x = x_i , s = 0 and for x = x_{i 1}, s = 1.

Also, dx = hds. We get

now,

Hence, we have

.....................1.4

These methods are called Adams-Bashforth methods.